1. Field of the Invention
The present invention provides a method and system for measuring electron densities in a plasma processing system, such as is used in semiconductor processing systems.
2. Description of the Background
Following the Second World War, several university research groups used microwave technology that had been developed during the war to study partially ionized gases. In particular, Professor Sanborn C. Brown""s group at Massachusetts Institute of Technology developed and exploited the so-called xe2x80x9ccavity techniquexe2x80x9d for the measurement of electron density in partially ionized, electrically quasi-neutral gases, which have come to be called plasmas.
In this procedure, changes in the resonant behavior of a microwave cavity were studied as a consequence of the presence of a plasma within it. Typically, a right, circularly cylindrical cavity operating in its lowest or nearly lowest order resonant mode was used, and the gas was contained within a coaxial Pyrex(trademark) or quartz tube. An aperture was provided in each planar end surface to permit passage of the tube through the cavity.
The presence of a plasma within a microwave cavity will, in general, affect both the resonant frequency of a particular cavity mode and the sharpness (Q) of the resonance; i.e., the precision with which the frequency of a microwave signal must be fixed if the resonant mode is to be appreciably excited. Using a form of perturbation theory, it is possible to relate the changes in these parameters to the electron density and the electron collision frequency in the plasma. The perturbation theory is valid only for (radian) frequencies xcfx89 that satisfy the condition:
xcfx892 greater than  greater than xcfx89p2xe2x89xa13.18xc3x97109Ne
where xcfx89p is the plasma (radian) frequency, and Ne is the electron density in electrons/cm3. Consequently, for the diagnosis of plasmas with electron densities of the order of 1012 cmxe2x88x923, the magnitudes of interest here, a microwave signal frequency (xcfx89/2Π) in excess of tens of GHz is required.
The requirement of signal frequencies on the order of tens of GHz causes a significant problem. The physical dimensions of a cavity designed to resonate in its lowest or nearly lowest order resonant mode are on the order of the wavelength of the signal. Thus, a cavity designed to resonate at about 35 GHz has dimensions on the order of only a centimeter. The use of such a small cavity for electron density measurements is difficult.
In principle it is possible to use a cavity designed to resonate in a xe2x80x9chigher orderxe2x80x9d mode to overcome the problem associated with the small physical size of a lowest or low order mode. However, if this approach is taken, it becomes extremely difficult to know with certainty the identity of a particular excited cavity mode. Consequently, it becomes practically very difficult, if not impossible, to apply perturbation theory to determine the electron density and the electron collision frequency.
One way to circumvent this problem is to use an xe2x80x9copenxe2x80x9d resonator, i.e., a resonator in which the electromagnetic field is not confined by a (nearly) completely enclosing conducting surface. A practical example of an open resonator is a pair of large aperture, circularly symmetrical end mirrors, with planar or curved surfaces and with no confining circularly symmetrical conducting surface between them. Open resonators of this type were considered in great detail by A. G. Fox and T. Li in xe2x80x9cResonant modes in a MASER interferometer,xe2x80x9d Bell System Technical Journal, vol. 40, pp. 453-488, March 1961. They showed that any mode that could be regarded as including a plane wave component propagating at a significant angle with respect to the axis of symmetry would not be appreciably excited, i.e., would have a very low Q. In effect, for an open resonator, the number of practically useful modes with resonant frequencies in a particular frequency range is far less than the equivalent number for a closed resonator of similar size. This property of open resonators provided an enormous opportunity for researchers to extend resonant plasma diagnostic techniques to frequencies above 35 GHz.
Microwave energy may be coupled from a waveguide feed to an open resonator using the same principles that govern coupling from a waveguide feed to a closed resonator. The location, spatial rotation, and size of a coupling aperture in a resonator mirror has to be appropriately related to the configuration of the electromagnetic field for the desired resonator mode. The input and output coupling apertures may both be on the same mirror or the input aperture may be on one mirror and the output aperture on the other.
Known electronically tunable microwave oscillators are frequency stabilized with the aid of a resonant cavity and a microwave discriminator. The basic concepts are documented in detail in various M.I.T. Radiation Laboratory Reports and in the Radiation Laboratory Series published by McGraw-Hill in 1947. One use of those oscillators is to cause an electronically tunable oscillator to track the resonant frequency of a microwave resonator as that frequency is changed. An extensive discussion of the techniques is presented in Vol. 11, Technique of Microwave Measurements, M.I.T. Radiation Laboratory Series, Carol H. Montgomery, Editor, McGraw-Hill Book Company, New York, 1947, pp. 58-78 (hereinafter xe2x80x9cMontgomeryxe2x80x9d). The entire contents of Montgomery are hereby incorporated by reference. A block diagram for a stabilization circuit 102 is shown in FIG. 1. FIG. 1 is similar to FIG. 2.29 on page 60 of Montgomery. The use of a microwave interferometer is also described in two known publications: (1) xe2x80x9cA Microwave Interferometer for Density Measurement Stabilization in Process Plasmas,xe2x80x9d by Pearson et al., Materials Research Society Symposium Proceedings, Vol. 117 (Eds. Hays et al.), 1988, pgs. 311-317, and (2) xe2x80x9c1-millimeter wave interferometer for the measurement of line integral electron density on TFTR,xe2x80x9d by Efthimion et al., Rev. Sci. Instrum. 56 (5), May 1985, pgs. 908-910.
When the frequency of the oscillator 100 differs from the resonant frequency of the microwave cavity 105, a signal is produced by the discriminator 110. The output of the discriminator 110 is amplified by an amplifier 115. The amplified discriminator signal 120 is then fed to the oscillator 100 with the polarity required to move the frequency of the oscillator 100 toward the resonant frequency of the microwave cavity 105.
If the frequency of the oscillator 100 is locked to the resonant frequency of the microwave cavity 105 using the stabilization circuit 102, tuning the microwave cavity 105 will cause the oscillator 100 to track the resonant frequency within a range that will be limited by the electronic tuning capability of the amplifier 115 and the frequency sensitivity of the ancillary microwave circuitry. Page 69 of Montgomery discloses a tunable oscillator.
As shown in FIG. 1, the major components of the stabilization system 102 are the microwave discriminator 110 and the amplifier 115. Two configurations for the discriminator 110 exist. FIG. 2 shows a first embodiment of the discriminator 110 that includes a directional coupler 150 and a bridge 160 (also known as a magic Tee). The bridge 160 compares the signal reflected by a short-circuited waveguide 165 of length x with the signal reflected from the microwave cavity 105 fed by a line 175 of length xxe2x88x92xcexg/8, where xcexg is the guide wavelength. The microwave signal enters the bridge 160 at arm 180 (the H-plane arm) through the directional coupler 150. The arm of the directional coupler 150 is the input to the discriminator from the microwave oscillator 100. At the Tee junction 185 of the bridge 160, waves of equal amplitude and phase traveling away from the junction are excited in the short-circuited waveguide 165 and the line 175 (collectively called the S arms).
In the second embodiment, the microwave discriminator 110 may also be realized by replacing the directional coupler 150 with a second magic Tee. This is not surprising since a magic Tee is equivalent to a 3 dB directional coupler. Thus, the analyses are similar and will not be considered further herein.
It is an object of the present invention to provide an improved plasma electron density measurement and control system using a microwave oscillator locked to an open resonator containing a plasma.
It is another object of the present invention to provide a robust control of the plasma electron density by tracking to another resonant mode when the oscillator loses its lock on one resonant mode.
These and other objects of the present invention are achieved by using a frequency stabilization system to lock the frequency of a local oscillator to a pre-selected resonant frequency of an open microwave resonator when the resonant frequency changes due to the introduction of a plasma within the open resonator.